$A$ vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects? Give examples in support of your answer.

(N/A) No; Yes; No.
Generally speaking,a vector does not have a definite location in space. This is because a vector remains invariant when displaced in such a way that its magnitude and direction remain the same. However,a position vector has a definite location in space.
$A$ vector can vary with time. For example,the displacement vector of a particle moving with a certain velocity varies with time.
Two equal vectors located at different locations in space need not produce the same physical effect. For example,two equal forces acting on an object at different points can cause the body to rotate,whereas their combination might produce a different turning effect (torque) depending on the point of application.